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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1225.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1225.g1 | 1225g2 | \([1, 0, 1, -5202076, -4567245077]\) | \(-162677523113838677\) | \(-95703125\) | \([]\) | \(8880\) | \(2.0752\) | |
1225.g2 | 1225g1 | \([1, 0, 1, -201, 1173]\) | \(-9317\) | \(-95703125\) | \([]\) | \(240\) | \(0.26974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1225.g have rank \(1\).
Complex multiplication
The elliptic curves in class 1225.g do not have complex multiplication.Modular form 1225.2.a.g
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.